MathDB
Reciprocal tangencies

Source: 2022 Switzerland IMO TST, Problem 2

August 1, 2022
tangencycollinearquadrilateralgeometrySwitzerland TST

Problem Statement

Let ABCDABCD be a convex quadrilateral such that the circle with diameter ABAB is tangent to the line CDCD, and the circle with diameter CDCD is tangent to the line ABAB. Prove that the two intersection points of these circles and the point AC∩BDAC \cap BD are collinear.
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